Local correlations in coupled cat maps with space-time duality

Abstract

Abstract We study quantum and classical correlations between local observables in perturbed coupled cat map model. In spite of fully chaotic dynamics, local correlations can be calculated explicitly due to the presence of spatiotemporal symmetry. This symmetry restricts correlations to the ‘light rays’ because the causality applies both in time and in space. We obtain detailed form of correlations of 2 and 3 sites’ observables demonstrating that exponential decay holds, generically. Furthermore, for unperturbed, pure linear, map, correlations between classical observables with a finite support exhibit superfast decay—the correlations disappear completely after a finite time.